Export cycles material to unity
You will have to Bake the material before you can use it in unity. Specifically the color data from the material.
Well what pass holds the color data? That depends on how your material is set up. You might have to bake a Diffuse pass, a Glossy pass, or an Emission pass (those are the three most common passes, but there are 11 total passes).

If you are using a Diffused BSDF, Principled BSDF (non metallic),  and Toon BSDF shader then bake a Diffuse pass set to Color.
However the Anisotropic BSDF, Glass BSDF, Glossy BSDF, Hair BSDF, and Velvet BSDF shaders will all output a pure black Diffuse pass. For these you need to bake a Glossy pass set to Color.

If you have an emissive materiel, you will need to use (no surprise here) an Emit pass.

The interesting one is the Principled shader. When set to metallic, it too will be a pure black diffuse pass.



These here are the minimum steps to bake the color of a cycles material to a texture (I'm using a diffuse pass here). You may depending on your UV layout need to create another UV map. Possible to bake texture to new UV map?


With the object in question selected, open the UV/Image Editor and create a new image which will be used to bake to.
In the material nodes add a Image Texture node, select the image you just created and keep it the active node (light yellow outline).
In the Properties Window under the Render tab scroll down to the Bake heading. Change the Bake Type to Diffuse, and choose only the Color pass. Now press the large Bake button.